Graphical reduction of reaction networks by linear elimination of species

TL;DR

This paper presents a graphical method for reducing biochemical reaction networks by eliminating fast species through a linear approach, ensuring the reduced system retains realistic kinetics and conservation laws.

Contribution

It introduces a novel graphical reduction technique for reaction networks that simplifies models while preserving key properties, applicable to both small and large networks.

Findings

The reduced network maintains realistic kinetics.

The method applies to various biological systems.

Conservation laws are preserved in the reduction.

Abstract

The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are assumed effectively to be at steady state with respect to the "slow" species. Under this assumption the steady state equations can be used to eliminate the "fast" variables and a new ODE system with only the slow species can be obtained. We interpret a reduced system obtained by time-scale separation as the ODE system arising from a unique reaction network, by identification of a set of reactions and the corresponding rate functions. The procedure is graphically based and can easily be worked out by hand for small networks. For larger networks, we provide a pseudo-algorithm. We study properties of the reduced network, its kinetics and conservation laws, and show that the kinetics of the reduced network fulfil realistic assumptions, provided the original network does. We illustrate our results using biological examples such as substrate mechanisms, post-translational modification systems and networks with intermediates (transient) steps.